| Secret sharing derives from a secret to several shares which are distributed to a number of participants, then the secret can be rebuilt only by the predetermined participants access structure. In1979, Shamir and Blakely proposed (t, n) threshold schemes independently, the former’s scheme was based on the Lagrange interpolating polynomial, while the latter’s scheme was based on the linear projective geometry. There are many scholar have researched deeply in the secret sharing scheme by now. There are many different kinds of the secret sharing scheme had been proposed to suffice the reality applications, there are cheat-proof secret sharing, dynamic secret sharing, multi-secrets secret sharing, verifiable secret sharing and so on. Those secret sharing scheme have widely used in digital signature, electronic auction, electronic voting and so on.This paper conducts some research and exploration on the problems about constructing the secret sharing based on monotone span programs and electronic voting based on secret sharing, the research results of this paper are as follows:1. We construct a verifiable linear multi-secrets sharing scheme by reversible circulant matrix and discrete logarithm, the access structures of our secret sharing scheme could change belong to the reality’needs, so it has the ability of. At the same time, we provide our secret sharing scheme is perfect and ideal. Because of our scheme also is a Secret Sharing Homomorphisms’scheme, it has more security and practical utility in the reality applications.2. We construct an E-voting scheme base on secret sharing, the scheme have two advantages due to the utilization of the secret sharing scheme of this paper:The first, this E-voting scheme was construct based on the secret sharing scheme which had provide is ideal, so the E-voting scheme is security. The second:our E-voting scheme is multi-candidates and the authorities authorities access structure so flexible to adapt to different reality applications. |
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